4 ms·
Wouldn’t it be more interesting to find a prime number where changing any single digit (maybe besides the least significant one) would still be a prime? Call it
by booleandilemma 6y ago
Wouldn’t it be more interesting to find a prime number where changing any single digit (maybe besides the least significant one) would still be a prime? Call it a sturdy prime.
- deleted 6y ago[deleted]
- qsort 6y agoNo such numbers except a small number of trivial cases exist. In odd bases, n % 2 === (sum of the digits of n), and in even bases, n % (b-1) === (sum of the digits of n).
- kosievdmerwe 6y agoIf we weaken the condition, to allow you to choose the replacement digit there are definitely semi-sturdy primes. For instance, 23 is semi-sturdy as you can replace 2 by 1 or 3 by 9 and both 13 and 29 are prime. The interesting question then becomes: how many?
- qsort 6y agoThis is most likely an open problem. If there existed infinitely many 'semi-sturdy' primes, this would imply that several prime 2-tuples match infinitely many primes, but results in that area are limited AFAIK.